Exponential Functions and Their Properties

The video tutorial covers exponential functions and their inverses. It begins with an introduction to exponential functions, followed by graphing examples of y=2^x, y=3^x, and y=4^x using tables of values. The tutorial then explores the concept of inverse functions, demonstrating how to graph them by switching ordered pairs. Key properties such as horizontal asymptotes, increasing and decreasing functions, and reflections across the y-axis are discussed. The video concludes with a comparison of exponential functions with bases greater than one and those between zero and one.

What is the primary focus of the video tutorial?

• Trigonometric functions and their graphs

• Linear functions and their properties

• Quadratic functions and their inverses

• Exponential functions and their inverses

When graphing y = 2^x, what is the y-value when x = -3?

• 1/8

• 1/4

• 1

• 1/2

Which of the following is true for the graph of y = 3^x?

• It is a decreasing function

• It passes through the point (0, 0)

• It has a horizontal asymptote at y = 3

• It is an increasing function

What is the common ratio between successive y-values for y = 4^x?

• 4

• 5

• 3

• 2

What happens to the graph of y = (1/2)^x as x increases?

• It increases

• It decreases

• It remains constant

• It oscillates

Which statement is true about the y-intercept of exponential functions?

• It is always 0

• It is always 1

• It is always negative

• It depends on the base

What is the domain of all exponential functions discussed?

• All real numbers

• x < 0

• x > 0

• x = 0

How do you find the inverse of an exponential function?

• Multiply the function by -1

• Switch the x and y values

• Divide the function by its base

• Add a constant to the function

What is the relationship between y = a^x and y = (1/a)^x?

• They are identical

• They are reflections across the x-axis

• They are reflections across the y-axis

• They are inverses of each other

What is the line of reflection for the inverse of an exponential function?

• y = x

• x = 0

• x = y

• y = 0